The Point of the Project

You are a portfolio manager, and you are trying to put together a portfolio that is designed to beat the market (represented here by the S&P 500 index). To do this you will first pick ten stocks, and then you will figure out how much of each of them to buy, using monthly data from the last five years to make your decisions. You have 100 million dollars to play with and you will pick stocks before the start of trading on August 8^th.

You will decide if you have beaten the S&P 500 by looking at the performance of your portfolio over the period August 8^th–November 8^th of this year (this is the ‘Evaluation Period’). To do this you will compare the risk-adjusted returns of your portfolio with the risk-adjustedreturn of the S&P. The project has three parts.

Project Part III

We are now going to find the optimal portfolio of risky stocks using the CAPM. We will also evaluate your performance. You need to answer the following questions:

• (2 points) Find the optimal portfolio weights using CAPM inputs. Calculate the Sharpe Ratio. If your portfolio is extreme consider imposing short sale constraints.
• (2 points) Compare your optimal portfolio weights using CAPM to the historical weights (Project II). Which set of weights seems more reasonable? Which one would you select? Why?
• (2 points) You believe the CAPM is not the perfect model, but useful as a baseline. Continue using the CAPM for eight of your stocks, however, for the remaining two, substitute in your own estimates for expected returns. Give at least one reason why you think these inputs are reasonable. How does your optimal portfolio compare to the ‘pure’ CAPM portfolio in Question 1.
• (2 points) Re-estimate the betas for all the stocks using two years of monthly data. Are these better estimates of betas? What does your optimal portfolio look like with the 2-year betas?
• (3 points) Select an optimal portfolio. Explainwhy you select it over the alternatives.
• (2 points) Assume you invested in your optimal portfolio at the start of class and held it for almost three months (August 8, 2019 to November 8, 2019). Calculate the all the performance measures from class for your optimal portfolio: (i) Sharpe measure, (ii) M-squared, (iii) Treynor measure, (iv) alpha and (v) the appraisal ratio.
• (2 points) Did your portfolio in #6 beat the market? Why? Which performance measure is the most appropriate? Why?
• (3 points) Your client asks you whythe portfolio weights you are recommending make sense. Provide a short and intuitive answer to his question. Use at most 100 words.